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Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods

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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 114))

Abstract

In this survey article, we will give a short summary of the basic algorithm issues of discontinuous Galerkin methods for time-dependent convection dominated problems. We will then give a few representative examples of recent developments of discontinuous Galerkin methods for such problems, and provide comparisons with several other types of numerical methods commonly used for similar or related problems. For the comparison, we concentrate mainly on the methods presented in the London Mathematical Society EPSRC Durham Symposium on Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations.

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Acknowledgements

The research of the author is supported partially by NSF grant DMS-1418750 and DOE grant DE-FG02-08ER25863.

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  1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

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  1. Department of Mathematics & Statistics, University of Strathclyde, Glasgow, United Kingdom

    Gabriel R. Barrenechea

  2. Istituto di Matematica Applicata e Tecnologie Informatiche - Pavia, Consiglio Nazionale delle Ricerche, Pavia, Italy

    Franco Brezzi

  3. Department of Mathematics, University of Leicester, Leicester, United Kingdom

    Andrea Cangiani

  4. Department of Mathematics, National Technical University of Athens, Zografou, Greece

    Emmanuil H. Georgoulis

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Shu, CW. (2016). Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods. In: Barrenechea, G., Brezzi, F., Cangiani, A., Georgoulis, E. (eds) Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-41640-3_12

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